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Best proximity point theorems: exposition of a significant non-linear programming problem

JOURNAL OF GLOBAL OPTIMIZATION 2013年第4期56卷 1699-1705页

作者： Basha, S. Sadiq Shahzad, N. Jeyaraj, R. Anna Univ Dept Math Madras 600025 Tamil Nadu India King Abdulaziz Univ Dept Math Jeddah 21589 Saudi Arabia St Josephs Coll Higher Secondary Sch Tiruchirappalli 620002 India

The primary goal of this work is to address the non-linear programming problem of globally minimizing the real valued function x -> d(x, Tx) where T is presumed to be a non-self mapping that is a generalized proximal contraction in the setting of a metric space. Indeed, an iterative algorithm is presented to determine a solution of the preceding non-linear programming problem that focuses on global optimization. As a sequel, one can compute optimal approximate solutions to some fixed point equations and optimal solutions to some unconstrained non-linear programming problems.

关键词： Global optimization non-linear programming problem Best proximity point Optimal approximate solution Generalized proximal contraction Proximal contraction Fixed point

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Best proximity point theorems: exposition of a significant non-linear programming problem

Best proximity point theorems: exposition of a significant n...

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8th International Tri-Annual Conference on Optimization - Techniques and Applications (ICOTA)

关键词： Global optimization non-linear programming problem Best proximity point Optimal approximate solution Generalized proximal contraction Proximal contraction Fixed point

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Solution of a non-linear programming problem with quadratic functions

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Optimization 1994年第1期29卷 33-43页

作者： Nenakhov, E.I. Primak, M.E. Institute of Cybernetics Prosp. Academica Glushkova 40 252207 Kiev-207 Ukraine Temple University Philadelphia United States

A problem of finding a vector of maximum length in a set determined by the intersection of a finite collection of balls is studied. Sufficient conditions for the problem to be solvable by non-combinatoric methods are formulated. In this case the ball problem can be reduced to a special convex programming problem. Some examples of the problem with violation of the sufficient conditions are considered. In general case of the ball problem a branch-and-bound method is proposed. © 1994, Taylor & Francis Group, LLC. All rights reserved.

关键词： ball global extremum inversion transformation local extremum non-linear programming problem

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A nonlinear programming approach to solve MADM problem with triangular fuzzy preference and non-preference information

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OPTIMIZATION AND ENGINEERING 2021年第2期22卷 1091-1116页

作者： Mehlawat, Mukesh Kumar Gupta, Pankaj Ahemad, Faizan Univ Delhi Dept Operat Res Delhi 110007 India

In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding to lower, middle, and upper limits of the triangular fuzzy numbers. The optimization problems corresponding to lower and upper limits are solved to obtain corresponding limits of basic triangular fuzzy multiplicative preference weights (TFMPWs) and basic triangular fuzzy multiplicative non-preference weights (TFMNPWs). The obtained optimal weight values are used to find the modal values of TFMPWs and TFMNPWs that helps in the ranking of the alternatives. The working of the proposed approach is demonstrated by solving a MADM problem from the literature. Furthermore, to validate the superiority of the proposed approach, a comparative analysis with similar existing approaches has been provided. The obtained results reveal the applicability and usefulness of the proposed approach.

关键词： non-linear programming problem Multi-attribute decision making Triangular fuzzy preference and non-preference relations Triangular fuzzy multiplicative weights Triangular intuitionistic fuzzy numbers

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Best proximity point theorems: unriddling a special nonlinear programming problem

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TOP 2014年第2期22卷 543-553页

作者： Basha, S. Sadiq Anna Univ Dept Math Madras 600025 Tamil Nadu India

This paper addresses the non-linear programming problem of globally minimizing the real valued function x -> d(x,Sx) where S is a generalized proximal contraction in the setting of a metric space. Eventually, one c... 详细信息

关键词： Global optimization non-linear programming problem Optimal approximate solution Best proximity point Fixed point Proximal contraction Generalized proximal contraction Proximal cyclic contraction Generalized proximal cyclic contraction

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Fuzzy linear programming problem with fuzzy decision variables: A geometrical approach

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JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2021年第4期24卷 853-863页

作者： Tadesse, Admasu Acharya, M. M. Sahoo, Manoranjan Acharya, Srikumar KIIT Univ Sch Appl Sci Dept Math Bhubaneswar 751024 Odisha India

Decision making problems force the decision maker to consider fuzzy decision variables in a fuzzy linear programming problem. Therefore, the proposed fuzzy linear programming problem considers a triangular fuzzy decision variable with triangular fuzzy parameters. A defuzzyfication method based on incenter of a triangle, which is formed by joining the vertices of the triangular fuzzy parameters and fuzzy decision variables. The coordinate of the incenter is obtained by using the concept of geometry. In next step, the incenter is considered as a vector quantity. Using the concept of obtaining the magnitude of a vector, the final mathematical model is formulated. The final mathematical programming problem is a crisp non-linear programming problem. The resultant crisp mathematical programming problem is solved by appropriate mathematical software. A numerical example is presented to illustrate the methodology.

关键词： Triangular fuzzy number Fuzzy decision variable non-linear programming problem

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Voltage Source Converter Based High-voltage DC System Modeling for Optimal Power Flow Studies

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2012年第3期40卷 312-320页

作者： Pizano-Martinez, Alejandro Fuerte-Esquivel, Claudio R. Angeles-Camacho, Cesar Univ Nacl Autonoma Mexico Inst Ingn Mexico City 04510 DF Mexico Univ Guanajuato Fac Elect Engn Guanajuato Mexico Univ Michoacana San Nicolas Hidalgo UMSNH Fac Elect Engn Morelia Michoacan Mexico

This article presents an enhanced model of a two-terminal voltage source converter based high-voltage DC system suitable for optimal power flow analysis in electric power systems. Both the back-to-back and the point-to-point voltage source converter and high-voltage DC schemes are addressed. Unlike to other proposals, the new model considers the operational constraints associated with the MVA ratings of the converters. The proposed model is implemented in a Newton-based optimal power flow approach and tested on the Baja California North 160-bus realistic power system. Simulation results show that a practically feasible optimal power flow solution can be obtained by considering the MVA converters' limits.

关键词： voltage source converter and high-voltage DC systems optimal power flow non-linear programming problem

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Evolutionary Game Theory in Multi-Objective Optimization problem

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2010年第Sup1期3卷 74-87页

作者： Jin, Maozhu Lei, Xia Du, Jian Sichuan Univ Sch Business Chengdu 610065 Peoples R China Univ Elect Sci & Technol China Natl Key Lab Commun Chengdu 610065 Peoples R China

Multi-objective optimization focuses on simultaneous optimization of multiple targets. Evolutionary game theory transforms the optimization problem into game strategic problem and using adaptable dynamic game evolution process intelligently obtains the optimized strategy. The problem of multiple frequency offsets estimation in distributed multiple inputs and multiple outputs system is real-world multi-objective search and optimization problems which are naturally posed as non-linear programming problems having multiple objectives. Simulation results evidence the proposed algorithm is superior to other algorithms with more robust convergence and environmental applicability.

关键词： Multi-Objective Optimization Evolutionary game non-linear programming problem Distributed multiple inputs and multiple outputs

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Ascent trajectory planning on-board based on direct optimisation method

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2013年第4期19卷 388-395页

作者： Lu, Xuefang Wang, Yongji Huazhong Univ Sci & Technol Dept Control Sci & Engn Key Lab Minist Educ Image Proc & Intelligent Control Wuhan Hubei Peoples R China

In this paper, an on-board trajectory planning algorithm is proposed for atmospheric ascent. To deal with the impact of disturbance, the on-board trajectory planning algorithm updates the reference trajectory by solving an optimal control problem on-board. Considering the strong non-linear aerodynamic, the optimal control problem is transformed into non-linear programming problem by trajectory discretisation. The direct optimisation method is implemented for this non-linear programming problem. Due to the small amount of discrete nodes and the initial guess solution which is close to the optimisation solution, the direct optimisation method is fast enough to generate a new reference trajectory in every guidance cycle. With different cases of the aerodynamic coefficient bias, numerical simulation for the generic hypersonic vehicle model and scramjet engine is done. The results show the accuracy and the effectiveness of the on-board trajectory planning algorithm.

关键词： trajectory planning ascent direct optimisation non-linear programming problem

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A method to solve Pythagorean fuzzy transportation problems

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2023年第5期14卷 1847-1854页

作者： Bhatia, Tanveen Kaur Kumar, Amit Appadoo, S. S. Sharma, M. K. Thapar Inst Engn & Technol Sch Math Patiala 147004 Punjab India Univ Manitoba Asper Sch Business Dept Supply Chain Management Winnipeg MB Canada

Nagar et al. (Int J Syst Assur Eng Manag (2021). https://***/10.1007/s13198-021-01339-w) proposed a method to solve Pythagorean fuzzy transportation problems (transportation problems in which the unit transportation cost for supplying the product from a source to a destination is represented by a Pythagorean fuzzy number. Whereas, all other parameters are represented by a non-negative real number). Nagar et al. also claimed that their proposed method is more efficient as compared to the existing methods (Complex Intell Syst (2019) 5: 255-263, Adalya J (2020) 9(1): 1301-1308). In this paper, it is pointed out that in all these existing methods, some mathematical incorrect assumptions are considered. Therefore, it is inappropriate to use these existing methods to solve Pythagorean fuzzy transportation problems. To resolve the inappropriateness of these existing methods, a new method (named as Mehar method) is proposed to solve Pythagorean fuzzy transportation problems.

关键词： Pythagorean fuzzy numbers Pythagorean fuzzy transportation problem (PyFTP) Crisp transportation problem (CTP) non-linear programming problem

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